Answer:
[tex]\sf y = \dfrac{1}{2}x - 5 [/tex]
Step-by-step explanation:
To find the equation of the line passing through the points (4, -3) and (-6, -8), we first need to determine the slope of the line using the formula:
[tex]\sf m = \dfrac{{y_2 - y_1}}{{x_2 - x_1}} [/tex]
where [tex]\sf (x_1, y_1) [/tex] and [tex]\sf (x_2, y_2) [/tex] are the coordinates of the given points.
Let's substitute the coordinates of the given points into the formula:
[tex]\sf m = \dfrac{{-8 - (-3)}}{{-6 - 4}} [/tex]
[tex]\sf m = \dfrac{{-8 + 3}}{{-6 - 4}} [/tex]
[tex]\sf m = \dfrac{{-5}}{{-10}} [/tex]
[tex]\sf m = \dfrac{1}{2} [/tex]
Now that we have the slope [tex]\sf m = \dfrac{1}{2} [/tex], we can use the point-slope form of the equation of a line:
[tex]\sf y - y_1 = m(x - x_1) [/tex]
Let's choose one of the given points, say (4, -3), and substitute the values into the equation:
[tex]\sf y - (-3) = \dfrac{1}{2}(x - 4) [/tex]
[tex]\sf y + 3 = \dfrac{1}{2}(x - 4) [/tex]
Now, let's simplify this equation:
[tex]\sf y + 3 = \dfrac{1}{2}x - 2 [/tex]
[tex]\sf y = \dfrac{1}{2}x - 5 [/tex]
So, the equation of the line is:
[tex]\sf y = \dfrac{1}{2}x - 5 [/tex]
